But even as the withdrawal begins in the coming months, spending will remain at elevated levels. In fact, the savings in the first year will probably amount to less than $10 billion -- a fraction of the $443 billion tab the U.S. has already run up in Afghanistan.

According to an analysis conducted by Center for a New American Security researcher Travis Sharp, if the average number of troops in Afghanistan falls from the current level of about 102,000 to 85,000 over the next fiscal year, taxpayers would save $7 billion over the previous year's spending levels.

"Seven billion is really quite modest," said Sharp. "If people think taking out surge troops is the answer to the Pentagon's budget problems, they have another thing coming."

Because extracting troops and equipment from the battlefield is so expensive, savings from troop reductions will not start to make a real difference until the following year.

Under Obama's watch, spending in Afghanistan has skyrocketed, right along with troop levels.

The United States spent $43 billion on the war in 2008, seven years after hostilities began, according to a Congressional Research Service report. This year, spending will hit $118 billion. There were 33,000 troops on the ground in 2009. Now there are 102,000.

Some researchers have estimated that each soldier on the ground in Afghanistan costs the military as much as $1 million a year. That's the top-end range.

But there are other factors to consider.

For the military, one of the biggest cost drivers in simple geography. Afghanistan is home to some very, very rough terrain, no ports, and little in the way of infrastructure.

"It's a landlocked country and you have to truck everything in from somewhere," said Chris Hellman, senior research analyst at the National Priorities Project, who added that supply lines are often disrupted by Afghan militants.

Just because troops startleaving Afghanistan, those costs won't go away. And if combat forces leave, other kinds of spending might have to increase.

"We may see a shift in funding rather than a reduction," Hellman said. "We might just be moving money from combat accounts to support accounts."

Afghan security forces, for example, might get a funding boost as their duties expand. Already the United States has increased the money spent on that force from $1.3 billion in 2005 to $11.6 billion in 2011.

Hellman said U.S. taxpayers will be footing that bill for a long time. After all, the GDP of Afghanistan was only $27 billion in 2010, according to the CIA factbook.

And even the act of pulling soldiers out of the fight will cost, Sharp said, citing additional transportation and security spending necessary to complete the drawdown.